b+7/4b=9

Solution for b+7/4b=9 equation:

b+7/4b=9

We move all terms to the left:

b+7/4b-(9)=0


Domain of the equation: 4b!=0

b!=0/4

b!=0

b∈R


We multiply all the terms by the denominator


b*4b-9*4b+7=0

Wy multiply elements

4b^2-36b+7=0

a = 4; b = -36; c = +7;
Δ = b2-4ac
Δ = -362-4·4·7
Δ = 1184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1184}=\sqrt{16*74}=\sqrt{16}*\sqrt{74}=4\sqrt{74}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{74}}{2*4}=\frac{36-4\sqrt{74}}{8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{74}}{2*4}=\frac{36+4\sqrt{74}}{8}
$